ISSN 0006-3509, Biophysics, 2018, Vol. 63, No. 2, pp. 282–288. © Pleiades Publishing, Inc., 2018. Original Russian Text © I.M. Ageev, Yu.M. Rybin, G.G. Shishkin, 2018, published in Biofizika, 2018, Vol. 63, No. 2, pp. 382–391.
COMPLEX SYSTEMS BIOPHYSICS
Manifestation of Solar–Terrestrial Rhythms in Variations of the Electrical Conductivity of Water I. M. Ageeva, *, Yu. M. Rybina, and G. G. Shishkina, ** a
Moscow Aviation Institute (National Research University), Moscow, 125993 Russia *e-mail:
[email protected] **e-mail:
[email protected] Received March 2, 2017; in final form, April 28, 2017
Abstract⎯Variations of electrical conductivity of distilled water were continuously measured for 1 month. Long-period (up to 7 days or longer) variations were observed in electrical conductivity of water. The effect of temperature on the conductivity was minimized methodically and analytically. Temporal variations in distilled water conductivity were periodically observed to correlate with the intensity of solar radiation at a wavelength of 10.7 cm and variations in atmospheric pressure and global magnetic indices. Possible causes of the phenomena are discussed. Keywords: variations in conductivity of water, rhythms of geophysical parameters, correlation and spectra of temporal variations, solar–terrestrial rhythms DOI: 10.1134/S0006350918020021
INTRODUCTION An association of terrestrial processes with space phenomena has been demonstrated in many studies [1, 2]. New findings are continuously added to the available data, and new phenomena are observed to support the association, especially as the effect of space events on the Earth’s biosphere is concerned. Rhythmic changes in parameters are known to be characteristic of biological systems and the total biosphere. Statistical studies have shown that many biorhythms coincide with well-known heliogeophysical oscillatory processes, while it remains unclear how low-energy variations in parameters of external fields and radiations exert their effects on biosystems [2–4]. The dominant factors of space events that determine the responses of living organisms are still poorly understood. This may be explained by the facts that the role of weak influences is difficult to experimentally identify in the presence of intense noise from anthropogenic environments and that convincing theoretical paradigms are still lacking. Many experimental studies have focused on the effects of weak anthropogenic fields on biological systems and have confirmed their existence. Responses of living organisms to external influences have been associated with changes in the parameters of water and aqueous solutions present in organisms because physical parameters of water experience appreciable changes when exposed to extremely weak external factors, as has been observed in several experimental studies. The effects of low-frequency magnetic fields
and high-frequency electromagnetic fields have received special attention. The results of the studies and relevant references are available from several publications [3, 5–14]. However, long-period oscillations of water parameters have not been studied systematically. Works that focus on the problem are scarce and often involve technical mistakes, which preclude a correct interpretation of their results. However, the effect of space physical factors on water has been reliably demonstrated in several works [11, 15, 16]. A special place among them is occupied by studies of the Italian chemist G. Piccardi [17], who used the reaction of bismuth oxychloride precipitation in water as a test for effects of space factors. Based on numerous experiments, Piccardi has demonstrated that the rate of a simple chemical redox reaction (the rate of production and precipitation of bismuth oxychloride) correlates well with solar activity. Time series derived from Piccardi’s tests have been subject to spectral analysis and changes in the properties of water have been found to coincide in period with changes in geomagnetic and heliophysical factors [7]. It has been concluded that periodical changes in water properties may be responsible for biological rhythms. Vladimirsky et al. [2] have further analyzed Piccardi’s data and have shown that the rate of this reaction correlates with the passage of the Earth through different sectors of the interplanetary magnetic field. The problem of how physical factors of a natural origin affect water includes two interrelated problems,
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that is, what is the physical nature of the source of the effect and what mechanism sustains the effect of the source. The multiplicity of responses that extremely weak factors induce in biological systems indicates that a common agent (a receptor) mediates the responses. Water and aqueous structures probably act as a common receptor in the case of biological systems. The hypothesis cannot be reliably verified because the available experimental and theoretical data are insufficient. The Sun is known to be a primary source of non-anthropogenic influences. The solar wind disturbs the near-Earth space and, primarily, the magnetosphere, and variations in solar radiation of the ultraviolet and shorter-wavelength regions of the spectrum change ionosphere parameters. Secondary effects of these changes cause variations in geomagnetic field, atmospheric parameters, the strength of the Earth’s magnetic field, Schumann resonator parameters, and other effects that influence the parameters of water. In addition, certain roles may be played by cosmic rays, including solar radiation, and gravity effects from the Sun and the Moon. For the mechanism that sustains the effect of a source on water, changes that an external physical factor induces in the structure of water or the structures of hydrate shells of ions dissolved in water are now commonly thought to underlie the changes observed in water parameters. The problem is that water structures, as well as the structures of hydrate shells, are not fully understood; this issue is a matter of continuous discussion [18, 19]. It is clear that the mechanisms that sustain the effects of various factors on water are impossible to establish as long as reliable data on variations in water structure are lacking. Our experiments were aimed at studying the variation in electrical conductivity of water and the parameter was measured continuously for 1 month in different seasons of the year for the purpose. Four series of long-term measurements were performed in total, and several tens of shorter series (up to 10 days in duration) were carried out additionally. Our method of testing for effects differs from the methods employed by Piccardi and his followers, who used aqueous solutions and studied the results of chemical reactions, which depend not only on the solvent properties, but also on the properties of a solute. We used distilled water (a more chemically pure medium) and a physical measurement technique, which was expected to allow new findings. We assumed that the character of variations would make it possible to identify the secondary source that affects water and to determine the mechanism of changes in the parameters of water. MATERIALS AND METHODS The instruments used in the study have been described in detail elsewhere [20]. Signals proporBIOPHYSICS
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tional to the water conductivity and temperature were recorded from two heat-insulated detectors. An insulating passive thermostat with the detectors was placed in a separate dark room to prevent the effects of several factors, such as illuminance, air composition, and air humidity. The thermostat served to stabilize the rate of changes in water temperature at approximately ±0.02 K/h. A double shielding of the detectors substantially reduced the high-frequency component of electromagnetic fields. Thus, low-frequency electromagnetic oscillations and atmospheric pressure mostly affected the water. Two identical detectors (conductometric cells) with an inner volume of approximately 3 mL each were placed no more than 4 cm apart. Each detector was filled with distilled water with a specific conductivity of approximately 2 μS/cm; the water volume was 1 mL. The detectors were only partly filled with water because preliminary experiments showed that the effects described below (variations in electrical conductivity) were undetectable with detectors filled in full. The effects are possibly due to special properties of the near-surface water layer or the properties of the water–air interface. The differences in conductivity and temperature measurements between the two detectors were minor and were due to insignificant differences in their construction and graduation. The temperature gradient within the thermostat was considered to be negligibly low. Two detectors were used to rule out possible failures and to control artifacts. The signal identity demonstrates that measurements were correct and that an external factor accounts for the variations observed in parameters. Measurements were performed continuously in an automated mode, using special software for data recording and processing. Conductivity and temperature readings were recorded for 1 min every hour in all series of measurements. The relative accuracy of measurements with our hardware–software complex was no worse than ±0.001 μS/cm for specific conductivity of water and no worse than ±0.001°C for water temperature. The mean of each 1-min signal was included in the further analysis. Time series with 1-h intervals were thus obtained for water conductivity and temperature. The resulting dataset with hourly values of water conductivity and temperature was subject to preliminary mathematical processing to allow for conductivity changes due to actual minor changes in temperature and to exclude continuous conductivity drift. Temperature fluctuations leading to changes in conductivity were addressed under the assumption that conductivity linearly depends on the temperature; this assumption is true at minor temperature changes, which were no more than several degrees over the observation period (approximately 1 month) in our case. A correct compensation for temperature changes requires that the temperature coefficient of electrical
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Fig. 1. Temporal dependences of water conductivity in experimental series (a) Autumn-2014, (b) Winter-2015, (c) Spring-2015, and (d) Summer-2015.
conductivity be known. The coefficient is 2–3% per degree for distilled water at 20°C. The coefficient was not important to know exactly to study the character and parameters of conductivity changes and was consequently taken to be 2% in all cases. A conductivity trend was considered after correcting the results with respect to temperature. The conductivity almost linearly changed with time in all series of measurements as a result of dissolution of the electrodes and detector walls, interactions with air over the water surface, and other factors. By slightly changing the slope of the approximation line, it is possible to nearly fully eliminate the effect of temperature on changes in water conductivity (a coefficient of correlation lower than 10–3). Thus, an origin unrelated to temperature was consequently assumed for the conductivity fluctuations obtained as a result of the above procedures. RESULTS Time dependences of water conductivity (Fig. 1) were obtained by measuring the parameter in four series of approximately 30 days each and processing the results. The series of measurements were performed from August 28, 2014 to September 28, 2014 (Autumn 2014); from January 21, 2015 to February 22,
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Fig. 2. The spectra of temporal variations in water conductivity for experimental series (a) Autumn-2014, (b) Winter2015, (c) Spring-2015, and (d) Summer-2015. Dashed lines indicate the 1- and 7-day periods.
2015 (Winter 2015); from March 14, 2015 to April 14, 2015 (Spring 2015); and from June 5, 2015 to July 5, 2015 (Summer 2015). As is seen from Fig. 1, periodical variations in water conductivity were observed in each series of experiments. The mean variation amplitudes were ±2.5%. The temporal variation curves indicate that external factors affected water to cause periodical changes in its conductivity. A visual examination of the curves shows weekly and, in the majority of cases, daily fluctuations in conductivity. To get a clearer picture of the daily rhythm, the plots were aligned by the days of the week. Sundays are shaded. Figure 2 shows the variation spectra of water conductivity in the four series of measurements. The frequency is expressed in inverse hours; 1- and 7-day periods are shown with dashed lines. As is seen, certain frequencies, although with minor deviations, are consistently observed in all four series, while the total spectral pattern varies among the series. In addition to the graphic presentation, Table 1 summarizes the oscillation periods and relative intensities of the most distinct lines for the four series of measurements. Oscillation periods are expressed in days (numerator); the intensity of each spectral component was normalized to the maximal intensity (denominator). The weekly and daily periodicities of changes in water conductivity were most clearly seen when we BIOPHYSICS
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Table 1. Oscillation periods (days) and relative intensities of spectral lines in four series of measurements Series Spring-2015
6.49/1.0 3.25/0.38 2.36/0.15
6.92 3.46 2.36
1.74/0.18 1.40/0.06 1.16/0.09 1.07/0.03 0.997/0.13 0.87/0.06 0.79/0.015 0.70/0.02
1.73/0.13 1.44/0.12 1.18/0.08
1.73 1.41 1.165 1.075 0.998 0.86 0.78 0.69
Harmonics similar to those in water conductivity variations were observed in periodic variations in parameters of other factors, which are considered in more detail below. Consequently, the coefficient of correlation was sometimes quite high and, when one time series was shifted relatively to another, periodically changed in sign while passing through its maxi-
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Fig. 3. Temporal variations in water conductivity as revealed by the superposed epoch analysis. Sundays are shaded. BIOPHYSICS
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(http://forecast.izmiran.ru), parameters of Schumann resonator oscillations (http://sosrff.tsu.ru), and cosmic ray intensity (http://cosrays.izmiran.ru). Coefficients of correlation with water conductivity were additionally calculated for the particle-flux density and particle velocity of the solar wind in one series and were insignificant again. The finding does not rule out the possibility of such a correlation for other periods of time, but requires further investigation.
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Conductivity variation, conv. units
employed a synchronous detection procedure (a variant of superposed epoch analysis), which efficiently isolates a periodical signal in the presence of noise [21, 22]. The following algorithm of superposed epoch analysis was used. The time point 00:00 of the first Sunday was used as an initial (reference) point in each series of measurements. The mean conductivity deviations in the four series were then calculated for respective time points. The result produced by the algorithm is shown in Fig. 3; the spectrum of the resulting temporal variation, in Fig. 4. The presence of periods characteristic of solar–terrestrial rhythms [1, 2] in the variation spectra of water conductivity may additionally lead to a correlation between changes in water conductivity and changes in the above parameters of space physical factors. The problem of correlation has partly been addressed in our previous works [15, 23]. A spectral analysis showed that the variation periods of several factors substantially differed from those of the conductivity of water (at least in the periods of measurements). The coefficients of correlation (Pearson’s correlation coefficient is meant hereafter) were no more than 0.1–0.2. The factors included geomagnetic field induction
0.998/0.64 0.84/0.03 0.76/0.03 0.68/0.03
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2.69 2.33
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Mean
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6.73/1.0 3.36/0.55 2.24/0.26
Series Summer-2015
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Electrical conductivity, rel. units
Series Autumn-2014
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Fig. 4. Spectrum of temporal variations in water conductivity as revealed by the superposed epoch analysis. The respective periods are shown in days at the top of the spectrum.
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Time, h Fig. 5. Temporal variations in water conductivity (dashed line) and solar radiation intensity at a wavelength of 10.7 cm (solid line) for the Autumn-2014 measurement series.
mums and minimums. This circumstance renders it impossible to make any conclusion for an actual relationship between the phenomena in question. The coefficient of correlation significantly depends on the phase shift observed in the oscillations in question at the initial moment of measurements in these conditions; however, the details of the phenomenon also require further investigation. Wolf numbers and solar radiation at a wavelength of 10.7 cm. Figure 5 shows the variation in water conductivity in the first series of measurements along with the variation in solar radiation intensity at a wavelength of 10.7 cm; the variations were normalized to their means and shown in scale for convenience (the solid line is solar radiation; the dashed line is the conductivity of water). Radiation intensity values are available for the time points 17:00, 20:00, and 23:00 in the IZMIRAN database (http://forecast.izmiran.ru), and all conductivity values obtained at other time points were accordingly excluded from the time series of hourly measurements. A more broken variation curve was consequently observed for water conductivity (Fig. 5). The coefficient of correlation between the two time series was 0.465 in the two series of measurements. When the Winter-2015 and Spring-2015 measurement series were subject to a correlation analysis, negligibly low coefficients of correlation were established for the respective observation periods. In the case of the Summer-2015 measurement series, the coefficient of correlation was initially insignificant, but increased to 0.545 when the water-conductivity time series was shifted by 144 h (conductivity values were collated with earlier radiation intensity measurements). Geomagnetic field indices Kp and Ap. To collate our data with the Kp and Ap indices of the geomagnetic field, index values measured at 3-h intervals were
400 Time, h
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Fig. 6. Temporal variations in water conductivity (dashed line) and the Kp index (solid line) for the Autumn-2014 measurement series.
retrieved from the database available at http:// www.wdcb.ru/. Figure 6 shows the variations in water conductivity and changes in Kp index for the Autumn-2014 measurement series. Because substantial fluctuations are characteristic of the Ap and Kp indices and hinder their visual comparisons with our data, index values were approximated with quadratic polynomials over certain time intervals (smoothed) and then normalized to the means obtained for the respective intervals. A correlation of the two curves was detectable in certain periods of time (for instance, in the period between hours 150 and 400 in Fig. 6). Because the visible correlation was distorted in the other periods, the resulting coefficient of correlation over the total observation period was 0.34. Higher coefficients of correlation could be obtained by shifting the time series of conductivity and magnetic field indices relative to each other. As an example, a 7-day shift (water conductivity was collated with earlier index values) yielded a coefficient of 0.496 for a correlation of water conductivity with the Ap index in the first measurement series (without shifting, the coefficient of correlation between Ap and water conductivity was 0.386, similar to that in the case of the Kp index). Similar results were obtained for the other measurement series. As an example, a correlation was absent (K = –0.08) when the data were collated without shifting in the second series (Winter-2015). A 4.2day shift of the water conductivity curve yielded a negative correlation coefficient of –0.597. In the third series (Spring-2015), a correlation was not observed without shifting, while a 6.58-day shift led to a correlation with a coefficient of 0.498 and a 4.3-day shift in the opposite direction (the water conBIOPHYSICS
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Fig. 7. Temporal variations in water conductivity (dashed line) and atmospheric pressure (solid line) for the measurement series Winter-2015.
ductivity was collated with later index values) yielded a negative correlation coefficient of –0.359. In the fourth series (Summe-2015), the coefficient of correlation between the time series was 0.242 without shifting, while shifting of the water conductivity series relative to the magnetic field index series led to a correlation with a coefficient of 0.61. The results indicate that the correlations are determined to a great extent by the fact that the time series have similar variation periods [24]. In particular, this is evident from the finding that a positive correlation changes to negative at a certain shift of the time series. A visual comparison of the variation curves of water conductivity and magnetic field index prompts the idea that a common perturbing factor affects the variations and that its effect is distinct in certain periods of time and is masked by changes in its own parameters or another perturbing source in other periods. Atmospheric pressure. Of all meteorological factors that might affect the water samples, air temperature, humidity, and composition are possible to exclude from consideration because hermetic detectors were used in insulated conditions during measurements. However, an effect of atmospheric pressure could not be neglected because the polyethylene walls of the detector were not rigid enough to prevent changes in external pressure from affecting the pressure within the detector. Figure 7 shows the variation curves of water conductivity and atmospheric pressure for the Winter2015 measurement series. Periods of approximately 6.9 and 3.4 days were clearly detectable in the pressure variation spectrum (9- and 7-day periods have similarly been observed in pressure variations [25]). The time series were shifted by 3 h in Fig. 7 so that conductivity values are collated with later pressure values. The coefficient of correlation was 0.4. BIOPHYSICS
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The effect of atmospheric pressure showed the same features as the effects of other factors. As an example, a correlation observed in the Winter-2015 measurement series became undetectable in the series Spring-2015. Characteristic frequencies of pressure fluctuations correspond to periods of 10.97, 4.86, 3.99, and 3.13 days in that measurement period. The periods were not observed in the spectrum of water conductivity oscillations; the coefficient of correlation is –0.166 in the series. Thus, atmospheric pressure variations are not the sole cause of the variation in water conductivity, although an appreciable correlation of the two parameters is possible in certain periods. DISCUSSION The correlations periodically observed between water conductivity and Wolf numbers, radiation intensity at a wavelength of 10.7 cm, atmospheric pressure, and magnetic indices indicate that the variation in water conductivity is a manifestation of global synchronization, which means that variations with similar periods are detectable in parameters of unrelated processes. Global synchronization starts at the solar system scale and manifests itself in integer ratios of the orbital and rotation periods of planets and moons. Total synchrony of planetary movements has been hypothesized based on currently available data [26] and explained by a stability of corresponding synchronous movements [27]. Synchronization processes have been considered in detail [28]. Lack of a threshold in the intensity of interactions is a feature of synchronization [29]; i.e., two systems with similar frequencies synchronize when in any, even extremely weak, interaction. The limiting factors are synchronization time, which increases with the decreasing intensity of interaction, and noise, which exerts a desynchronizing effect. As a result of global synchronization, the wellknown solar period of approximately 7 days (onefourth of the solar-rotation period) is detectable in the variations of geophysical parameters, a huge number of biospheric processes, and even in social matters, such as the duration of a week [22, 30–32]. It is therefore not surprising that periods similar to those of variations in other natural parameters are observed in the variation in water conductivity. The features of the majority of synchronized natural processes are that their oscillations are unstable and that the oscillation periods slightly (by no more than 10%) change with time, as was also observed in our measurements [33]. Note that periodic variations of various parameters are detectable not only in their values, but also in the finer structure of the corresponding time series [34, 35]. We intended to identify the actual dominant physical factor that underlies the water conductivity variations observed in this work. However, the most plausible assumption is that a set of different natural factors
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exert their joint effect on water, which is highly sensitive to effects of various nature. The factors are primarily associated with solar radiation and the solar wind, leading to both characteristic global periods in conductivity oscillations and periodical distortions of synchronization with each of the factors. The primary factors cause a variety of secondary phenomena; some of the phenomena are also capable of affecting the water parameters. These factors include background electromagnetic radiation of various spectral bands, including low-frequency Schumann resonator oscillations, variations in the geomagnetic field, changes in the electrostatic field, etc. Further research will help to better understand the roles of all these factors. CONCLUSIONS A special hardware–software complex was used to record temporal variations in specific conductivity of distilled water at a nearly constant temperature. Data were collected in four series of measurements, each lasting approximately 30 days, within 1 year. Distinct periodicities were observed in the temporal variations of water electrical conductivity. An analysis of the spectral characteristics showed that weekly and daily periods dominate in the variations. A correlation analysis showed significant coefficients of correlation in some experiments for the correlation of temporal variations in water conductivity with variations in solar radiation at a wavelength of 10.7 cm, variations in global magnetic field indices Kp and Ap, and variations in atmospheric pressure. Periodic oscillations observed for electrical conductivity of water (and possibly occurring in its other parameters) and their correlation with oscillations of known heliogeophysical parameters may provide a better understanding of the nature of periodical processes in living organisms and the total biosphere. REFERENCES 1. B. M. Vladimirskii, N. A. Temur’yants, and V. S. Martynyuk, Space Weather and Our Life (Vek-2, Fryazino, 2004) [in Russian]. 2. V. S. Martynyuk, N. A. Temur’yants, and B. M. Vladimirskii, There is No Bad Weather in Nature: Space Weather in Our Life (Kiev, 2008) [in Russian]. 3. T. K. Breus, Doctoral Dissertation in Physics and Mathematics (Moscow, 2003). 4. T. K. Breus, V. N. Binhi. and A. A. Petrukovich, Phys. Usp. 59 (5), 502 (2016). 5. I. M. Ageev, G. G. Shishkin, S. M. Es’kin, and Yu. M. Rybin, Biomed. Tekhnol. Radioelectron., No. 8–9, 75 (2008). 6. O. V. Betskii, N. N. Lebedeva, and T. I. Kotrovskaya, Biomed. Tekhnol. Radioelectron., No. 1, 37 (2003). 7. P. V. Vasilik and A. K. Galitskii, Kibernet. Vychisl. Tekh., No. 66, 11 (1985). 8. V. F. Kiselev, A. M. Saletskii, and L. P. Semikhina, Teor. Eksp. Khim., No. 2, 252 (1988).
9. O. A. Ponomarev and E. E. Fesenko, Biophysics (Moscow) 45 (3), 379 (2000). 10. M. C. Amiri and A. A. Dadkhah, Colloids Surf., A 278 (1–3), 252 (2006). 11. L. Boulanger, Int. J. Biometeorol. No. 41, 137 (1998). 12. S. V. Gudkov, V. I. Bruskov, M. E. Astashev, et al., J. Phys. Chem. B 115 (23), 7693 (2011). 13. A. D. Kney and S. A. Parsons, Water Res. 40, 517 (2006). 14. I. Otsuka and S. Ozeki, J. Phys. Chem. B 110 (4), 1509 (2006). 15. I. M. Ageev, G. G. Shishkin, M. D. Bubnova, and Yu. M. Rybin, in Weak and Ultraweak Fields and Radiation in Biology and Medicine: Proc. VI International Congress (St. Petersburg, 2012), p. 38 [in Russian]. 16. E. A. Polyak, Biofizika 36 (4), 565 (1991). 17. G. Piccardi, in The Influence of Solar Activity on the Atmosphere and Biosphere of the Earth (Nauka, Moscow, 1971), pp. 141–147. 18. S. D. Zakharov and I. V. Mosyagina, Cluster Structure of Water (FIAN, Moscow, 2011) [in Russian]. 19. A. N. Smirnov and A. V. Syroeshkin, Ross. Khim. Zh. 48 (2), 125 (2004). 20. Yu. M. Rybin, I. M. Ageev, M. D. Bubnova, and G. G. Shishkin, Tr. Mosk. Aviats. Inst., No. 89, 1 (2016). 21. A. Guglielmi and O. Zotov, J. Atmospheric Sol.-Terr. Phys. 69, 1753 (2007). 22. O. D. Zotov, Fiz. Zemli, No. 12, 27 (2007). 23. I. M. Ageev, Yu. M. Rybin, and G. G. Shishkin, Moscow Univ. Phys. Bull. 71 (6), 556 (2016). 24. T. K. Breus and A. A. Konradov, in Atlas of Temporal Variations in Natural, Anthropogenic, and Social Processes (Yanus-K, Moscow, 2002), Vol. 3, pp. 516—524 [in Russian]. 25. Atlas of Temporal Variations in Natural, Anthropogenic, and Social Processes (Nauchnyi Mir, Moscow, 1998), Vol. 2. 26. A. M. Molchanov, in Current Problems in Celestial Mechanics and Astrodynamics (Nauka, Moscow, 1973), p. 340. 27. P. Goldreich, in Tides and Resonances in the Solar System (Mir, Moscow, 1975), p. 288. 28. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge Univ. Press, Cambridge, UK, 2001). 29. I. I. Blekhman, Synchronization in Nature and Technology (Nauka, Moscow, 1981) [in Russian]. 30. Atlas of Temporal Variations in Natural, Anthropogenic, and Social Processes (OIFZ RAN, Moscow, 1994), Vol. 1 [in Russian]. 31. Atlas of Temporal Variations in Natural, Anthropogenic, and Social Processes (Yanus-K, Moscow, 2002), Vol. 3. 32. G. A. Zherebtsov, V. A. Kovalenko, and S. I. Molodykh, Dokl. Akad. Nauk 394 (5), 606 (2004). 33. A. V. Shabel’nikov, in Atlas of Temporal Variations in Natural, Anthropogenic, and Social Processes (Nauchnyi Mir, Moscow, 1998), Vol. 2, pp. 57–58. 34. S. E. Shnoll, E. V. Pozharskii, V. A. Kolombet, et al., in Atlas of Temporal Variations in Natural, Anthropogenic, and Social Processes (Nauchnyi Mir, Moscow, 1998), Vol. 2, pp. 303–305. 35. S. E. Shnoll, T. A. Zenchenko, K. I. Zenchenko, et al., Phys.-Usp., 43 (2), 205 (2000).
Translated by T. Tkacheva BIOPHYSICS
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